year 10 , 11 , 12 words for math!
HSC (NSW Higher School Certificate) Math Concepts
Below is a selection of key concepts from the HSC Mathematics syllabuses (Standard, Advanced, Extension), each with a concise definition.
Concept | Definition |
|---|---|
Function and Graphs | A rule that assigns each input (x) exactly one output (f(x)); its graph is the set of points ((x, f(x))). |
Quadratic Functions | Polynomials of degree two, written (ax^2 + bx + c), whose graphs are parabolas. |
Trigonometric Ratios | Ratios of sides in right-angled triangles: |
Differentiation | The process of finding the derivative (f'(x)), which gives the instantaneous rate of change of (f). |
Integration | The reverse of differentiation; computes the area under a curve (y = f(x)) via the antiderivative (F). |
Statistical Measures | Numerical summaries of data: mean (average), median (middle), mode (most frequent), standard deviation (spread). |
Probability Rules | Laws governing randomness: |
– Addition rule: (P(A\cup B)=P(A)+P(B)-P(A\cap B))
– Multiplication rule: (P(A\cap B)=P(A),P(B\mid A)). | | Vector Geometry (2D/3D) | Quantities with magnitude and direction; operations include addition, scalar multiplication, dot product, cross product. | | Exponential and Logarithmic | Exponential functions (y = a^x) and their inverses, logarithms (\log_a(x)), satisfying (a^{\log_a(x)}=x). | | Financial Mathematics | Models for interest and loans, including simple interest (I = P,r,t) and compound interest (A = P(1 + r)^t). |
GCSE (UK General Certificate of Secondary Education) Math Concepts
A core set of topics you’ll encounter in GCSE Mathematics, with definitions aligned to the UK exam specifications.
Concept | Definition |
|---|---|
Fractions | Representation of a part of a whole as (\tfrac{a}{b}), where (a) is numerator and (b) denominator. |
Percentages | A fraction expressed with denominator 100; e.g., 45% means (\tfrac{45}{100}). |
Ratio and Proportion | Comparison of two quantities; proportion solves for equality between two ratios. |
Linear Equations | First-degree equations of the form (ax + b = 0), whose graph is a straight line. |
Pythagoras’ Theorem | In a right triangle, (a^2 + b^2 = c^2), where (c) is the hypotenuse. |
Circle Theorems | Properties of angles, tangents, and chords in a circle, such as the angle in a semicircle is 90°. |
Probability | Quantifying chance: (P = \tfrac{\text{number of favourable outcomes}}{\text{total outcomes}}). |
Data Representation | Visual displays like bar charts, histograms, pie charts, box plots to summarise data. |
Transformations | Rigidity-preserving moves: translation, rotation, reflection, enlargement (scaling). |
Indices and Standard Form | Laws of exponents ((a^m a^n = a^{m+n}), etc.) and expressing large/small numbers as (a\times10^n). |